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Two Modeling Strategies for Empirical Bayes Estimation

arXiv 1409.2677 ↗First posted 9 Sep 2014stat.MEcited by 16

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Abstract (arXiv)

Empirical Bayes methods use the data from parallel experiments, for instance, observations Xk~N(Thetak,1) for k=1,2,ldots,N, to estimate the conditional distributions Thetak|Xk. There are two main estimation strategies: modeling on the θ space, called "g-modeling" here, and modeling on the x space, called "f-modeling." The two approaches are described and compared. A series of computational formulas are developed to assess their frequentist accuracy. Several examples, both contrived and genuine, show the strengths and limitations of the two strategies.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Sep 2014.

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Citing papers per year: 2021: 2; 2022: 0; 2023: 2; 2024: 4; 2025: 3; 2026: 5.

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  1. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  2. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  3. 2021Sharp regret bounds for empirical Bayes and compound decision problemscited by 8
  4. 2023A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regressioncited by 4
  5. 2023A New Perspective On Denoising Based On Optimal Transportcited by 2
  6. 2025Distribution-dependent Generalization Bounds for Tuning Linear Regression Across Taskscited by 2
  7. 2025Variational Learning of Disentangled Representationscited by 1
  8. 2026Sharp Inequalities between Total Variation and Hellinger Distances for Gaussian Mixturescited by 1
  9. 2026Multi-Domain Empirical Bayes for Linearly-Mixed Causal Representationscited by 1
  10. 2026Simulation-Based Empirical Bayescited by 1
  11. 2021Nonparametric Empirical Bayes Estimation and Testing for Sparse and Heteroscedastic Signalscited by 0
  12. 2024Neural-g: A Deep Learning Framework for Mixing Density Estimationcited by 0
4 more
  1. 2024Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problemcited by 0
  2. 2025Distributional Shrinkage II: Higher-Order Scores Encode Brenier Mapcited by 0
  3. 2026A Flexible Empirical Bayes Approach to Generalized Linear Models, with Applications to Sparse Logistic Regressioncited by 0
  4. 2026Empirical Bayes for correlated Gaussian sequence modelcited by 0